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Mat. Sb., 1935, Volume 42, Number 2, Pages 199–216 (Mi msb6410)  

This article is cited in 56 scientific papers (total in 58 papers)

Théorèmes d'unicité pour l'équation de la chaleur

A. Tychonoff

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Received: 13.02.1935

Citation: A. Tychonoff, “Théorèmes d'unicité pour l'équation de la chaleur”, Mat. Sb., 42:2 (1935), 199–216

Citation in format AMSBIB
\by A.~Tychonoff
\paper Th\'eor\`emes d'unicit\'e pour l'\'equation de la chaleur
\jour Mat. Sb.
\yr 1935
\vol 42
\issue 2
\pages 199--216

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    This publication is cited in the following articles:
    1. Ya. I. Zhitomirskii, “Uniqueness classes of solutions of the Cauchy problem for linear equations with increasing coefficients”, Math. USSR-Izv., 1:4 (1967), 737–756  mathnet  crossref  mathscinet  zmath
    2. V. S. Vladimirov, Yu. N. Drozhzhinov, “Generalized Cauchy problem for an ultraparabolic equation”, Math. USSR-Izv., 1:6 (1967), 1285–1303  mathnet  crossref  mathscinet  zmath
    3. P. S. Aleksandrov, S. V. Fomin, “The work of Tikhonov in topology and functional analysis”, Russian Math. Surveys, 22:2 (1967), 110–113  mathnet  crossref  mathscinet  zmath
    4. V. I. Dmitriev, A. G. Sveshnikov, “Tikhonov's work on mathematical physics”, Russian Math. Surveys, 22:2 (1967), 113–123  mathnet  crossref  mathscinet  zmath
    5. V. G. Hryptun, “Classes of functions quasianalytic with respect to a linear hyperbolic operator of second order”, Math. USSR-Izv., 4:5 (1970), 1135–1150  mathnet  crossref  mathscinet  zmath
    6. A. S. Kalashnikov, “A problem without initial conditions for linear degenerate hyperbolic equations of second order with infinite domain of dependence”, Math. USSR-Sb., 17:4 (1972), 603–616  mathnet  crossref  mathscinet  zmath
    7. O. A. Oleinik, “O edinstvennosti reshenii zadachi Koshi dlya obschikh parabolicheskikh sistem v klassakh bystrorastuschikh funktsii”, UMN, 29:5(179) (1974), 229–230  mathnet  mathscinet  zmath
    8. O. A. Oleinik, G. A. Iosif'yan, “An analogue of Saint-Venant's principle and the uniqueness of solutions of boundary value problems for parabolic equations in unbounded domains”, Russian Math. Surveys, 31:6 (1976), 153–178  mathnet  crossref  mathscinet  zmath
    9. V. P. Palamodov, “The work of G. E. Shilov in the theory of generalized functions and differential equations”, Russian Math. Surveys, 33:4 (1978), 219–235  mathnet  crossref  mathscinet  zmath
    10. O. A. Oleinik, E. V. Radkevich, “The method of introducing a parameter in the study of evolutionary equations”, Russian Math. Surveys, 33:5 (1978), 7–84  mathnet  crossref  mathscinet  zmath
    11. A. S. Kalashnikov, “Classes of uniqueness for integrodifferential equations with volterra operators of convolution type”, Funct. Anal. Appl., 13:2 (1979), 143–144  mathnet  crossref  mathscinet  zmath
    12. A. K. Gushchin, “On the uniform stabilization of solutions of the second mixed problem for a parabolic equation”, Math. USSR-Sb., 47:2 (1984), 439–498  mathnet  crossref  mathscinet  zmath
    13. O. A. Oleinik, “Examples of the non-uniqueness of the solution of the boundary-value problem for a parabolic equation in an unbounded domain”, Russian Math. Surveys, 38:1 (1983), 209–210  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. A. G. Gagnidze, “On uniqueness classes of the solutions of boundary-value problems for second-order parabolic equations in an unbounded domain”, Russian Math. Surveys, 39:6 (1984), 209–210  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. Denisov V. Repnikov V., “The Stabilization of a Solution of a Cauchy-Problem for Parabolic Equations”, Differ. Equ., 20:1 (1984), 16–33  mathnet  isi
    16. Denisov V., “Stabilization of Time Means of a Solution of a Cauchy-Problem for a Singular Hyperbolic Equation”, Differ. Equ., 22:1 (1986), 24–33  mathnet  isi
    17. Denisov V., “Stabilization of Time Means of Solutions of a Cauchy-Problem for a Parabolic Equation”, Differ. Equ., 24:1 (1988), 33–42  mathnet  isi
    18. Cristev D., “A Generalized Phragmen-Lindelof Theorem for the Parabolic Differential-Equation”, 42, no. 8, 1989, 13–14  isi
    19. F. Kh. Mukminov, “On uniform stabilization of solutions of the first mixed problem for a parabolic equation”, Math. USSR-Sb., 71:2 (1992), 331–353  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    20. Yu. A. Dubinskii, “The Cauchy problem and pseudodifferential operators in the complex domain”, Russian Math. Surveys, 45:2 (1990), 95–128  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    21. V. F. Akulov, A. E. Shishkov, “On asymptotic properties of solutions of mixed problems for quasilinear parabolic equations in unbounded domains”, Math. USSR-Sb., 73:2 (1992), 557–567  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    22. A. I. Prilepko, A. B. Kostin, “On certain inverse problems for parabolic equations with final and integral observation”, Russian Acad. Sci. Sb. Math., 75:2 (1993), 473–490  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    23. V. V. Kurta, “A comparison principle for a family of quasilinear parabolic equations”, Russian Math. Surveys, 49:4 (1994), 165–166  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    24. D. G. Orlovskii, “Determination of a parameter of a parabolic equation in Hilbert's structure”, Math. Notes, 55:3 (1994), 312–317  mathnet  crossref  mathscinet  zmath  isi
    25. Kurta V., “On the Uniqueness of Solutions for the Cauchy-Problem for the 2nd-Order Quasi-Linear Parabolic Equations”, Dokl. Akad. Nauk, 337:5 (1994), 574–576  mathnet  isi
    26. Murata M., “Nonuniqueness of the Positive Dirichlet Problem for Parabolic Equations in Cylinders”, J. Funct. Anal., 135:2 (1996), 456–487  crossref  isi
    27. V. V. Kurta, “On analogues of Finn's maximum principle for solutions of parabolic equations”, Russian Math. Surveys, 52:6 (1997), 1307–1309  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    28. Kurta V., “On Qualitative Properties of Solutions of Some Classes of Quasilinear Parabolic Equations”, Nonlinear Anal.-Theory Methods Appl., 30:4 (1997), 2121–2131  crossref  isi
    29. Akhmetov, DR, “A criterion for existence of L-1-norms for higher-order derivatives of solutions to a homogeneous parabolic equation”, Siberian Mathematical Journal, 41:3 (2000), 405  mathnet  crossref  isi
    30. L. M. Kozhevnikova, “On uniqueness classes of solutions of the first mixed problem for a quasi-linear second-order parabolic system in an unbounded domain”, Izv. Math., 65:3 (2001), 469–484  mathnet  crossref  crossref  mathscinet  zmath
    31. R. V. Guseinov, “Problem without Initial Conditions for the Heat Equation”, Math. Notes, 76:6 (2004), 770–777  mathnet  crossref  crossref  mathscinet  zmath  isi
    32. I. V. Tikhonov, “Abstract Differential Null-Equations”, Funct. Anal. Appl., 38:2 (2004), 133–137  mathnet  crossref  crossref  mathscinet  zmath  isi
    33. A. Yu. Popov, I. V. Tikhonov, “Exponential solubility classes in a problem for the heat equation with a non-local condition for the time averages”, Sb. Math., 196:9 (2005), 1319–1348  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    34. I. V. Artamkin, “Generating functions for modular graphs and Burgers's equation”, Sb. Math., 196:12 (2005), 1715–1743  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    35. I. V. Tikhonov, Yu. S. Èidel'man, “Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term”, Math. Notes, 77:2 (2005), 246–262  mathnet  crossref  crossref  mathscinet  zmath  isi
    36. V. N. Denisov, “On the behaviour of solutions of parabolic equations for large values of time”, Russian Math. Surveys, 60:4 (2005), 721–790  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    37. A. M. Nakhushev, “O sovremennom sostoyanii kraevykh zadach so smescheniem dlya osnovnykh tipov uravnenii v chastnykh proizvodnykh”, Trudy Tretei Vserossiiskoi nauchnoi konferentsii (29–31 maya 2006 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, SamGTU, Samara, 2006, 170–173  mathnet
    38. Domanskaya G. Kolin'ko M. Lavrenyuk S., “A Parabolic Variational Inequality in Unbounded Domains”, Differ. Equ., 42:1 (2006), 68–87  mathnet  crossref  isi
    39. N. M. Bokalo, “Correctness of the first boundary-value problem and the Cauchy problem for some quasilinear parabolic systems without conditions at infinity”, J. Math. Sci. (N. Y.), 135:1 (2006), 2625–2636  mathnet  crossref  mathscinet  zmath
    40. L. M. Kozhevnikova, “Uniqueness classes for solutions in unbounded domains of the first mixed problem for the equation $u_t=Au$ with quasi-elliptic operator $A$”, Sb. Math., 198:1 (2007), 55–96  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    41. Akhmetov, DR, “L-1-estimates for the higher-order derivatives of solutions to parabolic equations subject to initial values of bounded total variation”, Communications on Pure and Applied Analysis, 6:4 (2007), 1051  crossref  isi
    42. Medvid' I. M., “Higher-Order Parabolic Variational Inequality in Unbounded Domains”, Ukr. Math. J., 60:7 (2008), 1114–1135  crossref  isi
    43. N. A. Aksenov, “The Cauchy Problem for Certain Systems of Operator-Differential Equations of Arbitrary Order in Locally Convex Spaces”, Math. Notes, 90:2 (2011), 175–188  mathnet  crossref  crossref  mathscinet  isi
    44. L. M. Kozhevnikova, “Examples of the Nonuniqueness of Solutions of the Mixed Problem for the Heat Equation in Unbounded Domains”, Math. Notes, 91:1 (2012), 58–64  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    45. Yu. A. Aminov, Ia. Nasedkina, “Conditions on a Surface $F^2\subset E^n$ to lie in $E^4$”, Zhurn. matem. fiz., anal., geom., 9:2 (2013), 127–149  mathnet  mathscinet
    46. V. F. Vil'danova, F. Kh. Mukminov, “Anisotropic uniqueness classes for a degenerate parabolic equation”, Sb. Math., 204:11 (2013), 1584–1597  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    47. A. R. Khashimov, S. Yakubov, “On some properties of Cauchy problem for non-stationary third order composite type equation”, Ufa Math. J., 6:4 (2014), 135–144  mathnet  crossref
    48. Jenaliyev M.H. Amangaliyeva M. Kosmakova M. Ramazanov M., “About Dirichlet Boundary Value Problem For the Heat Equation in the Infinite Angular Domain”, Bound. Value Probl., 2014, 213  crossref  isi
    49. A. Yaakbarieh, V. Zh. Sakbaev, “Correctness of a problem with initial conditions for parabolic differential-difference equations with shifts of time argument”, Russian Math. (Iz. VUZ), 59:4 (2015), 13–19  mathnet  crossref
    50. V. F. Vil'danova, F. Kh. Mukminov, “Täcklind uniqueness classes for heat equation on noncompact Riemannian manifolds”, Ufa Math. J., 7:2 (2015), 55–63  mathnet  crossref  isi  elib
    51. M. M. Amangalieva, M. T. Dzhenaliev, M. T. Kosmakova, M. I. Ramazanov, “On one homogeneous problem for the heat equation in an infinite angular domain”, Siberian Math. J., 56:6 (2015), 982–995  mathnet  crossref  crossref  mathscinet  isi  elib
    52. A. A. Konkov, “O printsipe maksimuma dlya odnogo klassa nelineinykh parabolicheskikh uravnenii”, Vestn. SamGU. Estestvennonauchn. ser., 2015, no. 6(128), 89–92  mathnet  elib
    53. A. V. Pskhu, “Uravnenie drobnoi diffuzii s operatorom diskretno raspredelennogo differentsirovaniya”, Sib. elektron. matem. izv., 13 (2016), 1078–1098  mathnet  crossref  mathscinet  zmath
    54. A. A. Kon'kov, “Maximum principle for nonlinear parabolic equations”, J. Math. Sci. (N. Y.), 234:4 (2018), 423–439  mathnet  crossref
    55. F. G. Khushtova, “K probleme edinstvennosti resheniya zadachi Koshi dlya uravneniya drobnoi diffuzii s operatorom Besselya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:4 (2018), 774–784  mathnet  crossref  elib
    56. P. V. Denisov, “Ob asimptotike srednikh ot resheniya zadachi Koshi dlya sistemy parabolicheskikh uravnenii”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 145, VINITI RAN, M., 2018, 110–113  mathnet  mathscinet
    57. Duezguen F.G., Mosconi S., Vespri V., “Anisotropic Sobolev Embeddings and the Speed of Propagation For Parabolic Equations”, J. Evol. Equ., 19:3 (2019), 845–882  crossref  isi
    58. N. N. Dobrovolskii, N. V. Larin, S. A. Skobeltsyn, L. A. Tolokonnikov, “O resheniyakh obratnykh zadach difraktsii zvukovykh voln”, Chebyshevskii sb., 20:3 (2019), 220–245  mathnet  crossref
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